Wait, are you saying you will be using this machine as a normal machine, only using TV instead of a monitor? Dont bother. A TV runs at some obscenely low resolution (like 400x300) so you cant really run anything on it. It works fine if you are using it in a tivo-like setup, but dont even bother if you want to use a TV to replace your monitor.
As for distro, it doesnt really matter I dont think. I just finished setting up MythTV (
www.mythtv.org, a PVR program, like Tivo), and used a knoppix based install (knoppmyth,
www.mysettopbox.tv) which is basically Debian. Having apt-get is nice. As for a card, I got an old ge-force with tv out on ebay for like $20, it works fine. IIRC, there is a program called nvtv that has a graphical config for the TV-out on a nvidia card. Personally, I would stick to nvidia cards in Linux, they tend to have better support. Poke around on the KnoppMyth and MythTV sites/forums/mailing lists for more info.